Lecture on Hicksian Demand

Introduction

• Presenter: John
• Topic: Introduction to Hicksian Demand (Compensated Demand)

Definition and Concept

• Hicksian Demand: Also known as compensated demand.
• Key Characteristics:
  • Determined by:
    • Price of the good in question
    • Price of another good
    • Fixed level of utility
  • Represents the cost-minimizing amount of a good required to maintain a fixed level of utility.
  • It informs how much compensation a consumer would need to maintain the same utility level if prices change.

Problem Statement

• Objective: Minimize the budget equation subject to a utility function at a fixed utility level.

Steps to Find Hicksian Demand

1. Define the Problem:
   • Minimize the budget constraint subject to the utility function at a fixed utility level.
   • Formulate the Lagrangian:
     • L = Budget equation ± λ(Fixed level of utility, ( U_{bar} ) - Utility function)
2. Take First Order Partials:
   • Compute the first-order partial derivatives of the Lagrangian.
   • Set them equal to 0.
3. Solve for λ, x₁, and x₂:
   • ( x_1 ) and ( x_2 ) are the Hicksian demands.
   • Use λ to find the Hicksian demands.

Summary

• Hicksian demand minimizes costs for a fixed utility level.
• It compensates for price changes to maintain the same level of utility.
• Finding Hicksian demand involves defining the problem, setting up the Lagrangian, taking partial derivatives, and solving for the variables.